when he can absolutely be in a relationship with Honoka and still clean for Yoshino. This shit doesn't make sense.
Tenchi: I'm not cleaning for Himarin, so you don't need to worry about me going over to her place every week to clean.
Kannai: (Looks at the former idol next door who is a 25 year old, curvier, more confident version of herself. Literally next door.)
Kannai: (Looks at the bikini model with DD's coming over on the regular to 'visit his little sister', gives him pinup shots of herself, and has stripped down her bikini in bedroom on multiple occasions and kiss him)
Kannai: ....She's not the one I'm worried about.
On a serious note:
Not really. Not in Japan. Being invited into someone's house is a big deal, especially if they're of the opposite sex, triply when its just the two of you.
I am not sure I can give you a proper analogy of the level of... trust and closeness this implies and how big of a deal it is to get a key to someone's place, and to be able to come and go into their home. I guess the closest analogy would be allowing someone to give you a full body, buttnaked just the towel folded for your butt, body massage.
So just think of it as about the level of Tenchi being a professional masseuse and saying "I'll have to stop giving Himari full body oil massages if Honoka and I start dating". He really wouldn't HAVE to, he's being professional and nothing untoward is happening (at least from his end) but the odds of his new girlfriend being totally cool with that situation is not above 50%.